Hypothesis Testing Using Rejection Region(s) In Exercises 37–42, (a) identify the claim and state H 0 and H a , (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic z, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. 37. Caffeine Content A consumer research organization states that the mean caffeine content per 12-ounce bottle of a population of caffeinated soft drinks is 37.7 milligrams. You want to test this claim. During your tests, you find that a random sample of thirty-six 12-ounce bottles of caffeinated soft drinks has a mean caffeine content of 36.4 milligrams. Assume the population standard deviation is 10.8 milligrams. At α = 0.01, can you reject the research organization’s claim? (Source: National Soft Drink Association)
Hypothesis Testing Using Rejection Region(s) In Exercises 37–42, (a) identify the claim and state H 0 and H a , (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic z, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. 37. Caffeine Content A consumer research organization states that the mean caffeine content per 12-ounce bottle of a population of caffeinated soft drinks is 37.7 milligrams. You want to test this claim. During your tests, you find that a random sample of thirty-six 12-ounce bottles of caffeinated soft drinks has a mean caffeine content of 36.4 milligrams. Assume the population standard deviation is 10.8 milligrams. At α = 0.01, can you reject the research organization’s claim? (Source: National Soft Drink Association)
Solution Summary: The claim is that the mean caffeine content per 12-ounce bottle of a population of caffeinated soft drinks is 37.7 milligrams.
Hypothesis Testing Using Rejection Region(s)In Exercises 37–42, (a) identify the claim and state H0and Ha, (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic z, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.
37. Caffeine Content A consumer research organization states that the mean caffeine content per 12-ounce bottle of a population of caffeinated soft drinks is 37.7 milligrams. You want to test this claim. During your tests, you find that a random sample of thirty-six 12-ounce bottles of caffeinated soft drinks has a mean caffeine content of 36.4 milligrams. Assume the population standard deviation is 10.8 milligrams. At α = 0.01, can you reject the research organization’s claim? (Source: National Soft Drink Association)
Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Hypothesis Testing and Confidence Intervals (FRM Part 1 – Book 2 – Chapter 5); Author: Analystprep;https://www.youtube.com/watch?v=vth3yZIUlGQ;License: Standard YouTube License, CC-BY